Ebook: Approximation and Computation: In Honor of Gradimir V. Milovanović

Approximation theory and numerical analysis are central to the creation of accurate computer simulations and mathematical models. Research in these areas can influence the computational techniques used in a variety of mathematical and computational sciences. This collection of contributed chapters, dedicated to the renowned mathematician Gradimir V. Milovanović, represent the recent work of experts in the fields of approximation theory and numerical analysis. These invited contributions describe new trends in these important areas of research including theoretic developments, new computational algorithms, and multidisciplinary applications. Special features of this volume: - Presents results and approximation methods in various computational settings including polynomial and orthogonal systems, analytic functions, and differential equations. - Provides a historical overview of approximation theory and many of its subdisciplines. - Contains new results from diverse areas of research spanning mathematics, engineering, and the computational sciences. "Approximation and Computation" is intended for mathematicians and researchers focusing on approximation theory and numerical analysis, but can also be a valuable resource to students and researchers in engineering and other computational and applied sciences.

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Approximation theory and numerical analysis are central to the creation of accurate computer simulations and mathematical models. Research in these areas can influence the computational techniques used in a variety of mathematical and computational sciences. This collection of contributed chapters, dedicated to the renowned mathematician Gradimir V. Milovanovi?, represent the recent work of experts in the fields of approximation theory and numerical analysis. These invited contributions describe new trends in these important areas of research including theoretic developments, new computational algorithms, and multidisciplinary applications. Special features of this volume: - Presents results and approximation methods in various computational settings including polynomial and orthogonal systems, analytic functions, and differential equations. - Provides a historical overview of approximation theory and many of its subdisciplines. - Contains new results from diverse areas of research spanning mathematics, engineering, and the computational sciences. "Approximation and Computation" is intended for mathematicians and researchers focusing on approximation theory and numerical analysis, but can also be a valuable resource to students and researchers in engineering and other computational and applied sciences.

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Approximation theory and numerical analysis are central to the creation of accurate computer simulations and mathematical models. Research in these areas can influence the computational techniques used in a variety of mathematical and computational sciences. This collection of contributed chapters, dedicated to the renowned mathematician Gradimir V. Milovanovi?, represent the recent work of experts in the fields of approximation theory and numerical analysis. These invited contributions describe new trends in these important areas of research including theoretic developments, new computational algorithms, and multidisciplinary applications. Special features of this volume: - Presents results and approximation methods in various computational settings including polynomial and orthogonal systems, analytic functions, and differential equations. - Provides a historical overview of approximation theory and many of its subdisciplines. - Contains new results from diverse areas of research spanning mathematics, engineering, and the computational sciences. "Approximation and Computation" is intended for mathematicians and researchers focusing on approximation theory and numerical analysis, but can also be a valuable resource to students and researchers in engineering and other computational and applied sciences.
Content:
Front Matter....Pages i-xvii
Front Matter....Pages 1-1
The Scientific Work of Gradimir V. Milovanovi?....Pages 3-32
My Collaboration with Gradimir V. Milovanovi?....Pages 33-43
On Some Major Trends in Mathematics....Pages 45-49
Front Matter....Pages 51-51
An Application of Sobolev Orthogonal Polynomials to the Computation of a Special Hankel Determinant....Pages 53-60
Extremal Problems for Polynomials in the Complex Plane....Pages 61-85
Energy of Graphs and Orthogonal Matrices....Pages 87-96
Interlacing Property of Zeros of Shifted Jacobi Polynomials....Pages 97-101
Trigonometric Orthogonal Systems....Pages 103-116
Experimental Mathematics Involving Orthogonal Polynomials....Pages 117-134
Compatibility of Continued Fraction Convergents with Pad? Approximants....Pages 135-144
Orthogonal Decomposition of Fractal Sets....Pages 145-156
Positive Trigonometric Sums and Starlike Functions....Pages 157-182
Front Matter....Pages 183-183
Quadrature Rules for Unbounded Intervals and Their Application to Integral Equations....Pages 185-208
Gauss-Type Quadrature Formulae for Parabolic Splines with Equidistant Knots....Pages 209-231
Approximation of the Hilbert Transform on the Real Line Using Freud Weights....Pages 233-252
The Remainder Term of Gauss–Tur?n Quadratures for Analytic Functions....Pages 253-266
Towards a General Error Theory of the Trapezoidal Rule....Pages 267-282
Front Matter....Pages 283-283
Finite Difference Method for a Parabolic Problem with Concentrated Capacity and Time-Dependent Operator....Pages 285-296
Adaptive Finite Element Approximation of the Francfort–Marigo Model of Brittle Fracture....Pages 297-310
A Nystr?m Method for Solving a Boundary Value Problem on [0, ?)....Pages 311-325
Front Matter....Pages 283-283
Finite Difference Approximation of a Hyperbolic Transmission Problem....Pages 327-337
Homeomorphisms and Fredholm Theory for Perturbations of Nonlinear Fredholm Maps of Index Zero and of A-Proper Maps with Applications....Pages 339-363
On a Class of Matrix Differential Equations with Polynomial Coefficients....Pages 365-383
Front Matter....Pages 385-390
Optimized Algorithm for Petviashvili’s Method for Finding Solitons in Photonic Lattices....Pages 391-391
Explicit Method for the Numerical Solution of the Fokker-Planck Equation of Filtered Phase Noise....Pages 393-400
Numerical Method for Computer Study of Liquid Phase Sintering: Densification Due to Gravity-Induced Skeletal Settling....Pages 401-407
Computer Algebra and Line Search....Pages 409-424
Roots of AG-bands....Pages 425-438
Context Hidden Markov Model for Named Entity Recognition....Pages 439-445
On the Interpolating Quadratic Spline....Pages 447-460
Visualization of Infinitesimal Bending of Curves....Pages 461-467
....Pages 469-480